# Given mean insolation, can one place an upper bound on the daily peak insolation?

Photovoltaic panels are rated under standard conditions: eg a $100\mathrm{W}$ panel if irradiated with $1000\mathrm{W}/\mathrm{m}^2$ at $25^\circ\mathrm{C}$.

When the cost effectiveness of photovoltaics is discussed one is often presented with daily irradiation maps averaged yearly or possibly monthly. This is fine for cost effectiveness calculations.

But in designing the power conversion electronics or effects of grid injection one cannot work with average values - they must be able to sustain peak powers that are possibly larger than the nominal power of the panels, right?

If so, by what factor are these electronics oversized? I cannot find any similar maps of the average daily peak irradiance.

Given the daily solar energy incident ($\mathrm{kW hr /m^2\cdot day}$) averaged either annually or monthly, can one place an upper bound on the daily peak irradiance ($\mathrm{W / m^2}$)?

I am particularly interested in Mediterranean countries.

You're absolutely right that annual mean power is by no means a useful guide to the peak power a panel might generate. You can find places on Earth where annual mean insolation is well below $100~W/m^2$, and places where it's higher than $250~W/m^2$: but at both those places, there will be times when peak insolation is $1000~W/m^2$ or more. And so all PV is rated to that peak insolation, at the very least. So, mean annual insolation (whether in $W/m^2$ or $kWh/m^2\cdot day$) is no guide at all to peak insolation.

For more on the peak rated power of the panels, let's look more closely at specific technologies. PV comes in two distinct flavours, one is concentrating PV, the other is plain PV. They're very different beasts, so I'll treat them differently.

## Concentrating PV

This is designed to sit behind lenses which concentrate sunlight. The cell and the electronics are rated at much much higher insolation levels: the highest-efficiency cell according to the 2013 January review of solar cell efficiency records had an efficiency of $44.0\pm{3}\%$, and that was measured at 942 peak suns: i.e. $942~000~W/m^2$

## Plain PV

Panels are rated under very specific test conditions: 25° Celsius; light levels of $1000~W/m^2$; and a spectrum that represents the sun having passed through an air mass with an index of 1.5 (AM1.5).

Irradiation of the panel can be higher than $1000~W/m^2$: if the sun's rays are normal to the panel, and there's a lot of ambient light, those will add, and insolation will be above $1000~W/m^2$.

If the temperature is below 25° Celsius, then panel output will be higher: each panel has a coefficient that you can usually get from the manufacturer's data sheet, which represents the % change in output for each one degree change in temperature: the lower the temperature, the higher the output. Different panel technologies have different factors:: the First Solar Series-3 thin-film panel has a temperature coefficient of maximum peak power of $-0.25\% / ^oC$, so a reduction of 20°C below standard test conditions will give an extra 5% power.

At higher altitudes, the air mass is lower, and that will give higher insolation levels in direct beam. You're also above the snow line, which means it's colder, and there's a lot of reflected light from the snow, as well as a lot of light from the direct beam. And people do take PV to the top of very high mountains, and the electronics have to survive. So they're typically rated to a much higher power than the panel's nominal rated output.

The electronics are typically very cheap, compared to the rest of the panel's components, so typically they'll be very highly over-sized, to account for all sorts of extreme operating conditions. A full PV array on a mountain in Switzerland was recording power at 130% of rated output without any problems.